非紧致气动噪声半空间传播基本解的边界积分方法

为了获得低马赫数流动诱发的非紧致气动噪声在半空间内传播的基本解,结合复等效源方法和边界元方法建立了半空间精确格林函数的边界积分方程,当半空间边界为刚度型阻抗边界时可避免奇异性积分。同时基于等效源方法提出一种半空间二维非紧致圆柱声散射模型,推导了静止介质中声散射基本解的理论表达式。对静止介质中的二维圆柱声散射,数值解在研究的频率与观察点处与理论解一致。采用数值方法计算二维圆柱绕流诱发的半空间声场基本解,结果显示半空间边界强化了声源的声辐射能力,小于马赫数0.2的介质运动对声传播的影响可以忽略。

Boundary integral method for fundamental solution of non-compact aerodynamic noise propagating in half-space

A tailored Green’s function satisfying the corresponding acoustic boundary conditions on all scattering surfaces can be used as the fundamental solution to predict aerodynamic noise.For the noise induced by a low Mach number flow above an infinite impedance plane,the tailored Green’s function is obtained by solving the linear wave equation in frequency domain with the free-space Green’s function.Numerical solutions applicable for an arbitrary shape of the non-compact scattering body are achieved with the boundary element method.And the effect of the infinite impedance plane is handled with the image source and the complex equivalent source methods to avoid the singular integral when the reflecting plane is spring-like surface impedance.Furthermore,a theoretical model,which is suitable for a two-dimensional non-compact cylinder over an infinite plane with acoustic hard-wall or impedance boundary conditions,is obtained with the use of the equivalent source method.For acoustic scattering from a two-dimensional cylindrical in stationary medium,the numerical solution corresponding to a point monopole source are in a good agreement with the analytical solution for all observer angles and wave numbers.Moreover,the fundamental solutions of the noise induced by a low Mach number flow past the cylinder are evaluated with the numerical approach.The results show that the infinite half-space boundary strengthens the radiation ability of the sound sources,and the medium moving at low Mach number less than 0.2 has little influence on sound propagation.